Estimations of Fourier Coefficients For Controlled Distortion of a Periodic Function
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910744632623104 |
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| author | Sluchak, Vladimir |
| author_facet | Sluchak, Vladimir |
| contents | There is a class of physical filtration processes where the input is adequately modeled by a continuous periodic function f (x) of bounded variation over its period, and the output depends only on certain harmonics of the Fourier expansion of f (x) in the orthogonal basis of trigonometric functions. One example is the discrete spectrum sound generation by a revolving body in a steady fluid flow. This type of sound can be controlled through the amplitudes of certain harmonics of the circular distribution of the inflow velocity. Attainable goals of such a controlled distortion of f (x) are formulated as fuzzy targets and required inequalities relating the integral characteristics of f (x) with the coefficients of the corresponding Fourier expansion are proven. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10376 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimations of Fourier Coefficients For Controlled Distortion of a Periodic Function Sluchak, Vladimir General Mathematics There is a class of physical filtration processes where the input is adequately modeled by a continuous periodic function f (x) of bounded variation over its period, and the output depends only on certain harmonics of the Fourier expansion of f (x) in the orthogonal basis of trigonometric functions. One example is the discrete spectrum sound generation by a revolving body in a steady fluid flow. This type of sound can be controlled through the amplitudes of certain harmonics of the circular distribution of the inflow velocity. Attainable goals of such a controlled distortion of f (x) are formulated as fuzzy targets and required inequalities relating the integral characteristics of f (x) with the coefficients of the corresponding Fourier expansion are proven. |
| title | Estimations of Fourier Coefficients For Controlled Distortion of a Periodic Function |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2412.10376 |